Abstract Applying the (infinite) density-matrix renormalisation group technique, we explore the effect of an explicit dimerisation on the ground-state phase diagram of the spin-1 XXZ chain with single-ion anisotropy D. We demonstrate that the Haldane phase between large-D and antiferromagnetic phases survives up to a critical dimerisation only. As a further new characteristic the dimerisation induces a direct continuous Ising quantum phase transition between the large-D and antiferromagnetic phases with central charge $c=1/2$ c = 1 / 2 , which terminates at a critical end-point where $c=7/10$ c = 7 / 10 . Calculating the critical exponents of the order parameter, neutral gap and spin–spin-correlation function, we find $\beta =1/8$ β = 1 / 8 (1/24), $\nu =1$ ν = 1 (5/9), and $\eta =1/4$ η = 1 / 4 (3/20), respectively, which proves the Ising (tricritical Ising) universality class in accordance with field-theoretical predictions.Abstract Applying the (infinite) density-matrix renormalisation group technique, we explore the effect of an explicit dimerisation on the ground-state phase diagram of the spin-1 XXZ chain with single-ion anisotropy D. We demonstrate that the Haldane phase between large-D and antiferromagnetic phases survives up to a critical dimerisation only. As a further new characteristic the dimerisation induces a direct continuous Ising quantum phase transition between the large-D and antiferromagnetic phases with central charge $$c=1/2$$ c = 1 / 2 , which terminates at a critical end-point where $$c=7/10$$ c = 7 / 10 . Calculating the critical exponents of the order parameter, neutral gap and spin–spin-correlation function, we find $$\beta =1/8$$ β = 1 / 8 (1/24), $$\nu =1$$ ν = 1 (5/9), and $$\eta =1/4$$ η = 1 / 4 (3/20), respectively, which proves the Ising (tricritical Ising) universality class in accordance with field-theoretical predictions.

arXiv:2104.06649The European Physical Journal Special TopicsApr 13, 20216 citations

First-order quantum phase transition in the orthogonal-dimer spin chain

昌久古賀, Akihisa Koga

Jan 1, 20000 citations

Counting Edge Modes with the Higher Berry Curvature: A Bulk Topological Order Parameter for Quantum Spin Chains

Adam J. McRoberts, Joe Crossley, Chris Hooley +1 more

We show that the higher Berry curvature (HBC) can be used to count the gapless edge modes created by an entanglement cut, and thus defines an integer-valued topological order parameter for quantum spin chains. Given an individual spin-chain Hamiltonian, we construct an extending family by interpolating to a reference product Néel state, and show that the integral of the HBC over this extension is equal to the ordinary Berry phase of half of the chain swept out in response to an \textit{infinitesimal} field. It thus counts the spin of the gapless edge modes exposed by the cut, and a change in its integer value signals a phase transition. We illustrate this with several examples: $S=1/2$ , $S=1$ , and $S=3/2$ spin-Peierls chains, which undergo `singlet flop' transitions between different patterns of dimerisation; the bilinear-biquadratic chain, which clarifies the connection to the strict symmetry-protected topological phases classification; and the staggered $J_1$ -- $J_2$ chain, which has both nearest-neighbour and third-neighbour patterns of singlets depending on the signs of the interactions.We show that the higher Berry curvature (HBC) can be used to count the gapless edge modes created by an entanglement cut, and thus defines an integer-valued topological order parameter for quantum spin chains. Given an individual spin-chain Hamiltonian, we construct an extending family by interpolating to a reference product Néel state, and show that the integral of the HBC over this extension is equal to the ordinary Berry phase of half of the chain swept out in response to an \textit{infinitesimal} field. It thus counts the spin of the gapless edge modes exposed by the cut, and a change in its integer value signals a phase transition. We illustrate this with several examples: $S=1/2$, $S=1$, and $S=3/2$ spin-Peierls chains, which undergo `singlet flop' transitions between different patterns of dimerisation; the bilinear-biquadratic chain, which clarifies the connection to the strict symmetry-protected topological phases classification; and the staggered $J_1$--$J_2$ chain, which has both nearest-neighbour and third-neighbour patterns of singlets depending on the signs of the interactions.

cond-mat.str-elCross-listedarXiv:2607.21705Jul 27, 20260 citations

Exact results on the dimerisation transition in SU(n) antiferromagnetic chains

Ian K. Affleck

The author shows that SU(n) antiferromagnetic chains (or equivalently SU(2) spin-s-chains with Hamiltonians which project out singlet states) are exactly equivalent to the n 2 -state quantum Potts chain (obtained from the transfer matrix for the 2D classical Potts model), for arbitrary n (or s with n=2s+1). This implies that the models are spontaneously dimerised with a finite gap for n<2 but have a unique ground state and vanishing gap for n<or=2. The n to 0 limit may have some bearing on the quantum-Hall-effect localisation transition.The author shows that SU(n) antiferromagnetic chains (or equivalently SU(2) spin-s-chains with Hamiltonians which project out singlet states) are exactly equivalent to the n 2 -state quantum Potts chain (obtained from the transfer matrix for the 2D classical Potts model), for arbitrary n (or s with n=2s+1). This implies that the models are spontaneously dimerised with a finite gap for n<2 but have a unique ground state and vanishing gap for n<or=2. The n to 0 limit may have some bearing on the quantum-Hall-effect localisation transition.

Journal of Physics Condensed MatterJan 15, 199061 citations

Quantum phase transitions in integer spin chains

A. Zheludev

Bulletin of the American Physical SocietyMar 16, 20060 citations

c=1/2

c = 1 / 2 , which terminates at a critical end-point where

c=7/10

c = 7 / 10 . Calculating the critical exponents of the order parameter, neutral gap and spin–spin-correlation function, we find

\beta =1/8

β = 1 / 8 (1/24),

\nu =1

ν = 1 (5/9), and

\eta =1/4

η = 1 / 4 (3/20), respectively, which proves the Ising (tricritical Ising) universality class in accordance with field-theoretical predictions.

S=1/2

S=1

, and

S=3/2

spin-Peierls chains, which undergo `singlet flop' transitions between different patterns of dimerisation; the bilinear-biquadratic chain, which clarifies the connection to the strict symmetry-protected topological phases classification; and the staggered

J_1

J_2

chain, which has both nearest-neighbour and third-neighbour patterns of singlets depending on the signs of the interactions.